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Proceedings Paper

Continuous analog of multiplicative algebraic reconstruction technique for computed tomography
Author(s): Kiyoko Tateishi; Yusaku Yamaguchi; Omar M. Abou Al-Ola; Takeshi Kojima; Tetsuya Yoshinaga
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Paper Abstract

We propose a hybrid dynamical system as a continuous analog to the block-iterative multiplicative algebraic reconstruction technique (BI-MART), which is a well-known iterative image reconstruction algorithm for computed tomography. The hybrid system is described by a switched nonlinear system with a piecewise smooth vector field or differential equation and, for consistent inverse problems, the convergence of non-negatively constrained solutions to a globally stable equilibrium is guaranteed by the Lyapunov theorem. Namely, we can prove theoretically that a weighted Kullback-Leibler divergence measure can be a common Lyapunov function for the switched system. We show that discretizing the differential equation by using the first-order approximation (Euler's method) based on the geometric multiplicative calculus leads to the same iterative formula of the BI-MART with the scaling parameter as a time-step of numerical discretization. The present paper is the first to reveal that a kind of iterative image reconstruction algorithm is constructed by the discretization of a continuous-time dynamical system for solving tomographic inverse problems. Iterative algorithms with not only the Euler method but also the Runge-Kutta methods of lower-orders applied for discretizing the continuous-time system can be used for image reconstruction. A numerical example showing the characteristics of the discretized iterative methods is presented.

Paper Details

Date Published: 30 March 2016
PDF: 8 pages
Proc. SPIE 9783, Medical Imaging 2016: Physics of Medical Imaging, 97834Q (30 March 2016); doi: 10.1117/12.2214598
Show Author Affiliations
Kiyoko Tateishi, St. Marianna Univ. School of Medicine Hospital (Japan)
Tokushima Univ. (Japan)
Yusaku Yamaguchi, Shikoku Medical Ctr. for Children and Adults (Japan)
Omar M. Abou Al-Ola, Tanta Univ. (Egypt)
Takeshi Kojima, Tokushima Univ. (Japan)
Tetsuya Yoshinaga, Tokushima Univ. (Japan)

Published in SPIE Proceedings Vol. 9783:
Medical Imaging 2016: Physics of Medical Imaging
Despina Kontos; Thomas G. Flohr, Editor(s)

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